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Appendix VI.

the outer and inner diameters respectively of a ring of width b.
The Moment of Inertia of the ring will be found by deducting the
I of the cylinder r\ from that of the cylinder r0 : so from previous
reasoning,

I of ring -        £(/o4-tf)

and, dividing by the weight

(rQ2 - r?)

MOMENTS OF INERTIA OF SOLIDS OF REVOLUTION.

'<st

TJU

I

Solid.

r*
r

= Wj X VOl.

inch Ib. units.

Cylinder

r 2
'0
r<>
wirJr0<

iv-pr^b
7.
^
2

r* + r?
JJ+7?
w&b(r*-rF)

rQ outside
i* ( o      » )
2
l~
2

n inside

The moment of inertia of any fly-wheel can now be calculated
by adding the moments of the separate parts; and the energy of
rotation is deduced by reference to equations (2) or (3).

Experimentally.—The Energy of Rotation may also be found
by direct experiment on the rotating solid. A fly-wheel A, Fig.
971, is fastened by a plate B to the ball-bearing hub c of a bi-
cycle, and is supported by the bracket D, held to the wall by
bolts. A small weight E is attached to a string wound round the
hub c, and serves by its fall to cause rotation of the fly-wheel.
Let the wheel be accurately balanced, so that it will rest equally
well ia any position, and let the frictional resistance of the ball-
bearing be quite inappreciable.
, The weight being w, the energy of the fall is wH foot pounds,```